CANTON - Count on Cantor

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One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.

1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4
3/1 3/2 3/3
4/1 4/2
5/1

In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

Input

The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.

Then, it contains a single number per line.

Output

You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.

Example

Input:
3
3
14
7

Output:
TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

hide comments
vladimira: 2017-02-18 14:40:44

Hello everyone. I've written script in python 3. 13 lines of code: one range loop, one sqrt use, one ceil, some ariphmetic and one print. Why my solution uses 30 MB when all other people < 10MB?

Last edit: 2017-02-18 14:48:18
nilabja16180: 2017-02-09 21:57:48

AC in one Go, Triangular Number is the key!!

arindam1234: 2017-01-21 19:03:03

AC!!! My 100th on spoj.

vengatesh15: 2017-01-20 07:53:12

AC in 1 go:-)

chickadee: 2017-01-11 05:13:30

This is just math (the nominator and denominator for given term n can be calculated by a formula).

scorpion_ajay: 2016-12-19 20:03:42

woooooh second ques with AC in one go :p
get the pattern and rest is your implementation skills, enjoy implementing this ; )

kira28: 2016-12-10 15:47:34

AC in 1 go... very good ad-hoc

codesok: 2016-12-03 14:41:04

TAKE PEN AND PAPER, DRAW AND OBSERVE CAREFULLY

esshuvo: 2016-11-01 17:43:46

Not only have to do "find out" what is said in the problem but also while implementing this problem is helpfull for the novice like me!

parthendo: 2016-10-06 21:32:26

Read CAREFULLY and it's AC ;)


Added by:Thanh-Vy Hua
Date:2005-02-27
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource: ACM South Eastern European Region 2004